Turbulent Equation Research Articles

Conductive and viscous sub-layers on forced convection and mechanism of critical heat flux during flow boiling of subcooled water in a platinum circular tube with 3 mm inner diameter and 32.7 mm heated length at high liquid Reynolds number

The turbulent heat transfer, the subcooled boiling heat transfer and the steady state CHF for a Pt-circular test tube of a 3 mm inner diameter and a 32.7 mm heated length are measured with a wide range of inlet subcooling and flow velocity at high liquid Reynolds number, i.e. Red = 2.35 × 104 to 1.12 × 105. For flow velocities ranging from 4.103 to 21.446 m/s, the inner surface temperature of the Pt circular test tube calculated by the steady one-dimensional heat conduction equation is compared with the value obtained from our turbulent heat transfer correlation equation and the numerical solution of the RANS equation (Reynolds mean Navier–Stokes simulation) of the k-ε turbulence model. The conduction sub-layer thicknesses from the non-boiling region to CHF are measured in the conduction sub-layer itself in the forced convection region and the thinner sub-layer dissipated by boiling evaporation in the nucleate boiling region. The nondimensional thicknesses of local and average conductive sub-layers and, the thicknesses and nondimensional thicknesses of local and average viscous sub-layers on forced convection are estimated from the thicknesses of local and average conductive sub-layers and Prandtl numbers evaluated at the calculated temperature of the first control volume on the heated surface. In addition, the thickness of the conductive sublayer at the CHF point is estimated from measurements at various flow velocities. The experimental values of the CHF are also compared with authors’ widely and precisely predictable correlations of critical heat flux during flow boiling of subcooled water and the corresponding theoretical values of the liquid sub-layer dry-out models suggested by other researchers, respectively. The authors’ correlations and other researchers’ theoretical values can represent the subcooled boiling CHFs obtained in this study within the ranges of −22.74 to −6.21% difference and −22.17 to 6.16% one, respectively. Proposals for the main mechanism of critical heat flux during flow boiling of subcooled water on vertical tubes are confirmed again at high liquid Reynolds numbers based on experimental data. The boiling transitions to film boiling at the subcooled water flow boiling in the Pt test tube of d = 3 mm and L = 32.7 mm is not due to heterogeneous spontaneous nucleation or hydro-dynamic instability, but to liquid sub-layer dry-out model at the steady-state CHF. It is similar to those for the Pt test tubes with d = 3 mm and L = 66.5 mm, and d = 3 mm and L = 100 mm.

CFD modeling of the [formula omitted] capture by range hood in a full-scale kitchen

Air quality criteria in residential houses are increasing continuously. Multiple studies tend to use commercial CFD software in order to predict and optimize the flow conditions in range hoods. Most of them modeled the range hood without considering the rotating fan. In the present work, a new open-source solver was developed using the OpenFoam libraries. It is based on a buoyancy Boussinesq solver and a turbulent passive scalar transport equation accounting for the heated CO2 extraction by the rotating fan, fully modeled using the Multiple reference frame (MRF) approach. The new solver is carefully validated against experimental results for three benchmark cases: a CO2 plume, a differential heated cavity and the performance curve of a rotating fan. The model has been confidently used to model the CO2 extraction in a realistic residential kitchen considering one to four burners on. An improvement of 30% in the capture efficiency is reached by increasing the extraction flowrate of the fan from 100 to 300 cfm. An extraction efficiency of 100% is observed for flowrates above 330 cfm.

Modeling Surface Riblets Skin Friction Reduction Effect with the Use of Computational Fluid Dynamics

Towards the minimization of fuel consumption and aicraft emissions reduction, many disruptive technologies have been proposed in aviation industry regarding the improvement of aircraft aerodynamic performance. Among others, these technologies involve innovative passive and active flow control methodologies and techniques. A passive flow control methodology which is studied in the current work is the implementation of riblets, which are inspired by shark skin morphology, on a NACA 0012 airfoil. The main purpose of riblets is to alter the boundary layer characteristics near the wall region in such a way that the total skin friction decreases, resulting in an overall drag reduction of the aircraft with a straightforward impact on fuel consumption and thus emissions. The riblets are implemented in the Reynolds Averaged Navier Stokes equations with appropriate source terms in the turbulent dissipation transport equation. Two turbulence models are used, the k-? SST linear eddy viscosity model and the Baseline Reynolds Stress model which also uses the transport equation of the specific rate of turbulence dissipation (?). The computational results are compared with available experimental data of NACA 0012 with surface riblets attached. Drag and skin friction coefficients are presented for various angles of attack and the maximum potential benefit from riblet use is evaluated regarding aerodynamic performance and consequently reduction of emissions and fuel consumption.

Sensitivity study of momentum and turbulence models for subcooled boiling phenomena simulation

This sensitivity analysis of the momentum and turbulence equations uses the Eulerian two-phase approach and intends to achieve a validated modeling for subcooled boiling flows. The studied regime is relevant to many industry applications and to the critical heat flux phenomenon, an important process for design and safety analyses of water-cooled nuclear power plants. Ascending water flows in heated circular pipes are modeled under subcooled boiling condition and applying a combination of computational multi-fluid dynamics (CMFD) models, each one for the estimation of specific terms of the governing equations. Turbulence closure, drag, lift, turbulent interaction, turbulent dispersion, wall lubrication and interfacial area models are investigated through variations around a reference model set defined based on the literature review, changing each model one at a time to study their impacts on the simulation results. Key parameters, such as void fraction and temperature profiles, are chosen for the evaluation of the results. Despite the difficulty of tracking the contributions of simultaneously applied models, the Legendre–Magnaudet lift force and the Burns et al. turbulent dispersion force models show good agreement with the experimental data of a flow at 4.5 MPa used for the quality verification of the simulations. These models are also applied for flows with pressures ranging from 1.5 to 15 MPa, and they lead to promising results. This study gives interesting insights on the influence of the distinct models composing momentum and turbulence calculations, contributing to the validation effort of the CMFD approach for subcooled boiling flows.

Computational study on the performance improvement of axial-flow pump by inlet guide vanes at part loads

In order to investigate the influence of adjustable inlet guide vanes on the hydraulic performance of axial-flow pump and impeller, the axial-flow pump with different inlet guide vane adjustable angles was simulated based on the RNG k-e turbulent model and Reynolds time-averaged equations. The multivariate non-linear regression prediction model was established about the effect of adjustable inlet guide vane on the hydraulic performance of axial-flow pump based on the numerical simulation. The performance curves of axial-flow pump with different inlet guide vane adjustable angles were obtained by calculation, showing that the performance curve shifts towards larger flow volume in case the guide vanes are turned from positive to negative angle. With the increase of inlet guide vane positive angle, the optimum operating of pump is closer to smaller operating condition, but the hydraulic efficiency of pump is lower. The larger the flow is, the larger the decreasing amplitude of pump efficiency is. With the decreases of inlet guide vane negative angle, the higher hydraulic efficiency of pump increases first then decreases. The inlet guide vane angle affects the axial velocity distribution of the blade trailing edge.

Hybrid computational aeroacoustics approach based on the synthetic turbulence model in Eulerian description

A low-cost hybrid computational aeroacoustics (CAA) approach based on the synthetic turbulence and acoustic perturbation equations (APE) is established. A statistic model based on Reynolds Averaged Navier-Stokes (RANS) simulation is introduced to generate the unsteady synthetic turbulence. The spatial correlation of the turbulence is realized via the spatial filtering of a white noise field. Instead of using the Lagrangian convective particles of the fast random particle-mesh (fRPM) method, the presented model is entirely established in Eulerian description by introducing a convection-attenuation equation of the synthesized turbulent velocity. Therefore, the same discretization is applied for both synthetic turbulence model and APE solver. Without the requirement of the interpolation between different discretization systems, this modified model is more concise to implement numerically and more accessible to extend to parallel processing. Since the convection-attenuation equation only operates in the sound source domain, additional boundary conditions are established. The recommended parameters for mesh generation are discussed through a validation case. The hybrid CAA approach based on the presented model is applied to the slat noise prediction of a two-dimensional high-lift airfoil. Good agreement is found through the comparison with the reference data, and the computational costs are acceptable.

Cylindrical porous radiant burner with internal combustion regime: Energy saving analysis using response surface method

Abstract A response surface analysis is performed on a cylindrical porous radiant burner with internal combustion regime, which is recently introduced. A structured grid is used to perform the simulations. First, the equations of continuity, momentum, turbulence, energy, radiation, mixture fraction and progress variable were solved with an appropriate accuracy. An excellent agreement was observed between the numerical results and the available laboratory data. Second, three response surfaces of the output enthalpy, radiant efficiency and radiative heat were investigated using the verified model. The independent variables including input power, porous foam’s emissivity and the equivalence ratio are changed in the ranges of P ∈ [1.5,5] kW, erad ∈ [0.4,0.9] and φ ∈ [0.5,1.1], respectively. The results show that the radiant efficiency of above 50% can be achieved using this type of porous burner with no preheating. Based on a local sensitivity analysis, the sensitivity of ηrad to erad and φ at (P,erad,φ) = (5,0.4,0.8) is equal to 7.50% and 0.511%, according to the coded independent variables, respectively. Moreover, according to an energy saving analysis, for a radiant heat of 900 W, 13.6% of energy could be saved compared to the ideal conditions, in which φ ≈ 1, by choosing the best conditions.

Design and numerical investigations of natural convection heat transfer of a new rippling fin shape

In the present work, a new fin shape is proposed to improve the convective heat transfer in heat sinks and to reduce their weight. The problem under consideration is a natural convection with air as the working fluid. Three-dimensional numerical simulations are carried out using FLUENT 19.0, to solve the continuity, momentum, turbulence, and energy equations to predict the flow and temperature field for different fins on a vertical base. Five configurations of rippling fins are considered with two aspect ratios and different heat flux inputs. The numerical results are compared to previous data available in the literature for a vertical rectangular finned plate (reference case) to validate the model. For each configuration, the heat sink temperature field and the natural convection driven air flow are discussed. The heat flux is varied from 519.396Wm2 to 4674.565Wm2. The overall thermal performance is characterized by the heat dissipation rate per unit mass. By comparison to conventional rectangular fin, the proposed fin geometry can reduce the temperature at the heat sink base by up to 18.35 K, increase the mass specific heat transfer coefficient by up to 101.41%, and decreases the thermal resistance by 9.81%. Within the scope of this study. The case with one ripple provides the best thermal performance. The results also showed that, the flow and heat transfer enhancements are a decreasing function of Rayleigh number. Overall, the heat transfer enhancement is better with rippling fins than with the rectangular fins, with a maximal mass reduction of 47%. The proposed models provide a practical alternative to the widely adopted plate fin heat sinks, which very promising for future thermal developments.

A bubble-induced turbulence model for gas-liquid bubbly flows in airlift columns, pipes and bubble columns

The presence of bubbles dramatically changes the liquid turbulence in bubbly flows. Modifications to liquid turbulent transport equations by adding source terms representing the effect of bubble-induced turbulence (BIT) are usually made to promote the reliability of Computational Fluid Dynamics simulations. However, existing closures for BIT fail to give reliable predictions of both mean flow properties and turbulence kinetic energy. In this work, a new BIT model, which embeds both the bubble swarm effects and the physics of bubble-induced vortices, is proposed to modify the Reynold stress model for bubbly flows. The anisotropy nature of BIT is also considered. The new BIT model can predict both mean flows and turbulence kinetic energy in airlift column systems, while investigated existing BIT models from the literature fail. Three simulation test cases for pipes and one for a bubble column have been conducted to show the validity of the proposed BIT model.

Towards a self-consistent Boltzmann's kinetic model of fluid turbulence

A closure for the effective relaxation time of the Boltzmann–BGK kinetic equation for fluid turbulence is presented, based on a double-averaging procedure over both kinetic and turbulent fluctuations. The resulting effective relaxation time appears to agree with values obtained via a renormalisation group treatment of the Navier–Stokes equation only at low values of k/T, the ratio of turbulent kinetic energy to fluid temperature. For the kinetic treatment delivers a significantly longer effective relaxation time.

Effect of changing the height of final step of the stepped chute on the flow profile in stilling basin using the VOF method

In this study, the effect of the geometry modification in the physical model (step height) on flow factors in the stilling basin is investigated numerically. The Navier–Stokes equations were used to solve the flow field; the Reynolds stress turbulence model was used to model Reynolds stresses, and the volume of fluid method was used to determine the surface flow profile. Momentum and turbulence equations have been solved by the finite volume method. The results indicate that when the height of the steps in the stilling basin increases, the flow depth increases, and eventually the flow velocity decreases. When the height of the steps decreases, the flow velocity increases, and the flow depth decreases. The results of the numerical model are in good enough agreement with experimental results.

On sustaining turbulence production in interacting supersonic streamwise vortices

Interacting supersonic streamwise vortices have been investigated as a means to enhance mixing at supersonic velocities. However, the turbulence dynamics associated with this class of flow has been left largely unexplored despite turbulence playing a major role in the achievement of molecular mixing. For this reason, the process of turbulent kinetic energy production in interacting supersonic streamwise vortices is investigated in this work. Specifically, the link between the mean flow motion and turbulence, represented by the production term of the turbulent transport equation, is analyzed. An approach is proposed in which the mean flow strain rates can be cast such that their intensity and morphology properly couple with the requirements imposed by the Reynolds stresses that, in the framework of this work, are shown to be intimately linked with the resulting plume morphology. The analysis is leveraged for the design of a mode of vortex interaction targeted to maintain a positive production of turbulent kinetic energy in the downstream evolution. The resulting configuration was experimentally investigated in a Mach 2.5 flow by stereoscopic particle image velocimetry. The results from these experiments show that the turbulence production remained positive and sustained turbulence levels, a unique result in the available literature. The role of turbulence anisotropy and the principal direction of negative planar strain rates are highlighted in detail in this work.

An analytical description of the energy balance in turbulent, round, free jets

This brief contribution provides a quantification of the terms of the turbulent kinetic energy transport equation for a round steady turbulent free jet. The analysis is based on the assumption of flow self-similarity, and it is performed by means of a simple analytical asymptotic analysis. The results are in good agreement with the experimental findings of Panchapakesan and Lumley [J. Fluid Mech. 246, 197–223 (1993)] and with the large eddy simulations of Bogey and Bailly [J. Fluid Mech. 627, 129–160 (2009)], hence providing a theoretical interpretation of such findings.

Experimental and numerical investigation of jet impingement cooling using extended jet holes

In this study, jet impingement cooling on flat surface was investigated experimentally. The aim of this study is to elucidate the effect of extended jet holes on the heat transfer performance of the in-line array jet impingement configuration. The studies were performed under fully turbulent flow condition (16250≤Re≤32500). Local Nusselt number (Nu) distribution on the surface of interest was obtained experimentally by using Transient Liquid Crystals (TLC) method. Numerical investigations were conducted as the same configuration with the experimental method to explore the flow and heat transfer characteristics. SST k-ω with low-Re correction turbulence model was used for solving turbulence equations. Experimental and numerical studies were conducted on 1×6 (in-line array) jet impingement cooling configuration. Dimensionless jet to jet spacing (Xn/Dj), dimensionless jet plate to target plate spacing (Z/Dj) and dimensionless target plate width (Y/Dj) were taken as 5.0, 6.0 and 6.0, respectively. Five different Gj/Dj (1.0, 2.0, 3.0, 4.0 and 5.0) were investigated and the results were compared with orifice plate jet impingement configuration (Z/Dj=Gj/Dj=6.0). Average and local Nu number distributions, pressure drop of the system, flow characteristics and Performance Evaluation Criterion (PEC) were examined in detail. Numerical results were compared with the experimental data and it was obtained that SST k-ω turbulence model was able to accurately predict the average and local Nu number distributions on the surface of interest. The maximum average and local Nu numbers were obtained on the condition of Gj/Dj=2.0. Furthermore, PEC shows that the most feasible dimensionless nozzle to target plate gap was Gj/Dj=2.0 at all Re numbers.

Numerical study on airflow temperature field in a high-temperature tunnel with insulation layer

Comprehensive understanding of the airflow temperature field in a high-temperature tunnel is critical for the deep underground engineering project. In this paper, we establish a two-dimensional axisymmetric model coupling the convective-conduction heat transfer based on the k - ε turbulence equation, by which the airflow temperature field in a high-temperature tunnel for geothermal mining is investigated. We compare the airflow temperature variation with or without thermal insulation layer (TIL) and introduce the valid ventilation distance (VVD) to quantify their differences. The sensitivity analysis of critical factors on the airflow temperature are also examined. We find that (1) the TIL has a remarkable insulation effect even in a high-temperature tunnel, and its insulation effect can be well quantified by the VVD; (2) the TIL insulation effect decreases dramatically as the rock temperature increases, resulting in an exponential decay in the VVD; (3) changing critical factors are effective for reducing the air temperature and increasing the VVD, but these impacts decrease rapidly as the rock temperature grows; (4) the established empirical formula facilitates the VVD estimation and favors parameter optimization in high-temperature tunnels of deep underground engineering projects.

Jet impingement cooling on a rib-roughened surface using extended jet holes

In this study, jet impingement cooling on a rib-roughened surface has been investigated experimentally. The aim of this study is to investigate the effect of extended jet holes on the heat transfer performance and flow characteristics of the jet impingement cooling on a rib-roughened surface. The studies have been conducted under turbulent flow condition (16,250 ≤ Rej ≤ 32,500). Transient Liquid Crystals (TLC) method has been employed to investigate the average and local Nusselt number (Nu) distributions on the surface of interest. Six inline arrays of jet impingement configuration have been examined as the jet impingement cooling system. Jet holes were extended towards the target surface with the nozzles. Various dimensionless nozzles to the target surface gaps (Gj/Dj = 1.0, 2.0, 3.0, 4.0 and 5.0) have been investigated. Rectangular cross-sectional ribs were located on the surface of interest for the augmentation of heat transfer. Experimental studies were conducted on the dimensionless rib height as Hr/Dj = 0.42. In addition, numerical studies were carried out to investigate the flow and heat transfer characteristics. The effect of various dimensionless rib heights (Hr/Dj) on convective heat transfer performance has also been investigated numerically. SST k-ω with low-Re correction turbulence model was used for solving turbulence equations. Average and local Nu number distributions, flow characteristics and Performance Evaluation Criterion (PEC) were examined in detail. Results were compared with the orifice plate (Gj/Dj = 6.0) jet impingement configuration. Results showed that SST k-ω turbulence model accurately reveals the experimental data. Application of extended jet holes is a feasible method for practical application of the jet impingement cooling, especially at relatively low dimensionless nozzle gap (Gj/Dj≤4.0). Furthermore, improperly designed rib height has been found to diminish heat transfer performance.

CFD supported performance analysis of an innovative biomass dryer

Abstract In this work, the thermo-fluid performance of a biomass drying chamber with innovative tray configurations has been numerically investigated by solving the governing equations of mass, momentum, energy, and turbulence using Fluent 17. The effect of tray number, tray length, tray arrangement, and hole arrangement on the tray surface has been examined in detail. An enhancement factor has been presented to account for the heat transfer and the associated pressure drop. The results show that both the heat transfer and the pressure drop increase with an increase in tray number and optimum tray number is decided based on the highest enhancement factor. Six different tray arrangements have been examined and it has been found that alternative packed side and rear-front walls arrangement of trays is most effective from the thermo-fluid performance point of view. Based on the hole arrangement investigation, it has been revealed that compared to the inline hole arrangement, the staggered arrangement resulted in higher heat transfer performance with almost no addition to pressure drop. Correlations have been developed to predict the enhancement factor for different tray lengths, tray numbers, and inline and staggered hole arrangements, which help design an efficient and economic biomass drying chamber.

Robust aerodynamic morphing shape optimization for high-lift missions

Morphing wings have a great potential to enhance the overall performances of the aircraft by adapting the wing shape to various flight conditions. However, there are some issues concerning the applicability of this idea at high-lift missions. An important problem is the need for more actuators along the airfoil that may face with the weight penalty. This mainly arises from the design parameterization methods that are unable to effectively control the leading and trailing edge deformations without modifying the middle part of the airfoil. In this work, a new parameterization method is presented for optimum morphing wing section design at high-lift missions that tends to minimize the number of actuators by increasing un-morphed middle sections of the wing. Genetic algorithm is used for shape optimization and the aerodynamic objective function is calculated by the numerical solution of the compressible turbulent flow equations. Results show that the new method is capable of generating high-lift morphing geometry with minimum shape transformation. In addition, higher lift coefficient is achieved in less computational time by the new method compared with the alternative flexible leading edge airfoil.

Analytical solution to the near wall turbulent energy equation

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Flow structure and turbulent kinetic energy of velocity fluctuations in a cylinder near wake at Re = 3900

SIV measurements of instantaneous vector fields of velocity have been performed in the near wake behind a circular cylinder in a cross flow at Re = 3900. Patterns of velocity profile evolution with the distance from the cylinder have been refined. Distributions of components of the turbulent production term of the turbulent kinetic energy transport equation have been estimated. Their main patterns and correlation with the formation and motion of large-scale vortices (Karman vortices) have been revealed.